3 ideas
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 21681 | Given all true atomic propositions, in theory every other truth can thereby be deduced [Russell] |
| Full Idea: Given all true atomic propositions, together with the fact that they are all, every other true proposition can theoretically be deduced by logical methods. | |
| From: Bertrand Russell (Intro to 2nd ed of Principia Mathematica [1925], p.xv) | |
| A reaction: This is evidently his strongest statement of the ideal underlying logical atomism. The atoms were initially sense-date, but then became atomic propositions saying an object has a property. |
| 1799 | If we can't know minds, we can't know if Pyrrho was a sceptic [Theodosius, by Diog. Laertius] |
| Full Idea: We can't say the school of Pyrrho is sceptical, because the motion of the mind in each individual is incomprehensible to others, so we don't know Pyrrho's disposition. | |
| From: report of Theodosius (Chapters on Scepticism [c.100 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.8 |